New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction

The snake-in-the-box problem asks for a longest induced path in the hypercube graph Q_n. We find a length-191 snake in dimension n=9—the lowest dimension where the maximum is unknown—improving the previous record of 190 that had stood for 14 years. We also establish new lower bounds in dimensions 10–13. To find these records, we introduce snakepits, collections of disjoint snakes, to expand the search space and open new routes between snakes. This motivates our new Snakepit-in-the-Box benchmark, which seeks maximal edge counts when allowing multiple components. Finally, we introduce Beam Anchor, a search-supervised learned constructor algorithm that finds 100 inequivalent length-190 snakes in dimension 9.